Computationally efficient transfinite patches with fullness control

TL;DR

This paper introduces a new Midpoint Coons transfinite patch that combines speed and control for representing complex surfaces efficiently, using a novel constrained parameterization.

Contribution

It proposes a fusion of two transfinite schemes into a single, efficient method with enhanced control, leveraging generalized barycentric coordinates.

Findings

Faster computation of transfinite patches

Improved control over surface representation

Effective in real-time design applications

Abstract

Transfinite patches provide a simple and elegant solution to the problem of representing non-four-sided continuous surfaces, which are useful in a variety of applications, such as curve network based design. Real-time responsiveness is essential in this context, and thus reducing the computation cost is an important concern. The Midpoint Coons (MC) patch presented in this paper is a fusion of two previous transfinite schemes, combining the speed of one with the superior control mechanism of the other. This is achieved using a new constrained parameterization based on generalized barycentric coordinates and transfinite blending functions.